Number of Hours for Pipe to Fill the Tank if the Drain is Closed

Problem 1
A pipe can fill a tank in 3 hours if the drain is open. If the pipe runs with the drain open for 1 hour and the drain is then closed, the tank will be filled in 40 minutes more. How long does it take the pipe to fill the tank if the drain is closed?
 

Problem 2
A pipe can fill a tank in 4 hours if the drain is open. The tank is initially empty. If the pipe runs with the drain open for 1 hour and the pipe is then closed, the tank will be emptied in 40 minutes more. How long does it take the pipe to fill the tank if the drain is closed?
 

Answer Key

 

A tank is supplied by two pipes A and B and emptied by a third pipe C

Situation
A tank is supplied by two pipes A and B and emptied by a third pipe C. If the tank is initially empty and all pipes are opened, the tank can be filled in 20 hours. If the tank is initially full and A and C are opened, the tank can be emptied in 4 hours. If the tank is initially full and B and C are opened, the tank can be emptied in 2 hours. Pipe A supplies 50 liters per minute more than B.
1.   Find the rate of pipe A in liters per minute.

A.   120 C.   110
B.   130 D.   140

2.   Find the rate of pipe C in liters per minute.

A.   170 C.   150
B.   160 D.   140

3.   Find the capacity of the tank in liters.

A.   12,000 C.   11,500
B.   12,500 D.   13,000

Work-related Problems

Case 1: Workers have different rates

Work rate × Time to finish the job = 1 job done

Work rate = (1 job done) / (Time to finish the job)

Time of doing the job = (1 job done) / (Work rate)

 

For example
Albert can finish a job in A days
Bryan can finish the same job in B days
Carlo can undo the job in C days